Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C2×C61×#2148 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C61 | #102 |
| commutator | C8 | C23×C4×C61 |
| Frattini, cosocle | C2×C8 | C24×C61 |
| socle | C22×C61 | C2×#102 |
| prime radical | C22×#135×C61 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C61 ◁ C23×C4×C61 ◁ C23×C8×C61 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(3,4,6,10,8,13,20,12)(5,14,17,28,18,31,15,30)(7,21,19,11,23,27,32,29)(9,22,25,16,26,33,24,34);(3,5)(4,9)(6,15)(7,22)(8,18)(10,24)(11,28)(12,25)(13,26)(14,27)(16,32)(17,20)(19,34)(21,31)(23,33)(29,30);(3,6,8,20)(4,10,13,12)(5,15,18,17)(7,19,23,32)(9,24,26,25)(11,27,29,21)(14,30,31,28)(16,22,34,33)3904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26379);